We present the results of a multiwavelength campaign for Mrk 501 performed in 1996 March with ASCA, EGRET, Whipple, and optical telescopes. The X-ray —ux observed with ASCA was 5 times higher than the quiescent level and gradually decreased by a factor of 2 during the observation in 1996 March. In the X-ray band, a spectral break was observed around 2 keV. We report here for the —rst time the detection of high-energy c-ray —ux from Mrk 501 with EGRET with 3.5 p signi—cance (E ( 100 MeV). Higher —ux was also observed in 1996 AprilMay, with 4.0 p signi—cance for E ( 100 MeV and 5.2 p signi—cance for E ( 500 MeV. The c-ray spectrum was measured to be —atter than most of the c-ray blazars. We —nd that the multiband spectrum in 1996 is consistent with that calculated from a one-zone synchrotron self-Compton (SSC) model in which X-rays are produced via synchrotron emission and c-rays are produced via inverse Compton scattering of synchrotron photons in a homogeneous region. The —ux of TeV c-rays is consistent with the predictions of the model if the decrease of the Compton scattering cross section in the Klein-Nishina regime is considered. In the context of this model, we investigate the values of the magnetic —eld strength and the beaming factor allowed by the obser- vational results. We compare the 1996 March multiwavelength spectrum with that in the —are state in 1997 April. Between these two epochs, the TeV —ux increase is well correlated with that observed in keV range. The keV and TeV amplitudes during the 1997 April —are are accurately reproduced by a one-zone SSC model, assuming that the population of synchrotron photons in 1996 are scattered by newly injected relativistic electrons having maximum energies of However, the TeV spectrum c max D 6 ) 106. observed during the 1996 March campaign is —atter than predicted by our models. We —nd that this cannot be explained by either higher order Comptonization or the contribution of the ii seed ˇˇ IR photons from the host galaxy for the —rst-order external radiation Comptonization, but we cannot exclude possible eUects of the IR photons that may arise in the parsec-size tori postulated to exist in active galactic nuclei. Subject headings: BL Lacertae objects: individual (Markarian 501) ¨ gamma rays: observations ¨ radiation mechanisms: nonthermalX-rays: galaxies